A109204 Minimal value of k>0 such that n^9 + k^2 is a semiprime.

2, 3, 5, 10, 5, 2, 11, 4, 7, 2, 9, 4, 7, 5, 3, 2, 7, 16, 7, 2, 39, 2, 25, 12, 5, 7, 21, 2, 5, 3, 7, 16, 9, 17, 5, 24, 19, 4, 3, 20, 7, 6, 11, 4, 3, 4, 17, 12, 17, 2, 7, 70, 3, 3, 5, 2, 11, 16, 5, 42, 7, 4, 3, 26, 3, 9, 25, 26, 9, 5, 33, 6, 23, 12, 23, 2, 9, 6, 7, 2, 23, 4, 3, 16, 11, 16, 9, 2, 3

Offset: 0

Author

Jonathan Vos Post, Jul 04 2005

Keywords

• easy
• nonn

Examples

			a(0) = 2 because 0^9 + 1^2 = 1 is not semiprime, but 0^9 + 2^2 = 4 = 2^2 is.
a(1) = 3 because 1^9 + 1^2 and 1^9 + 2^2 are not semiprime, but 1^9 + 3^2 = 10 = 2 * 5 is semiprime.
a(2) = 5 because 2^9 + 5^2 = 537 = 3 * 179 is semiprime, but 2^9 plus no smaller square is.
a(51) = 70 because 51^9 + 70^2 = 2334165173095351 = 43063 * 54203496577 and for no smaller k>0 is 51^9 + k^2 a semiprime.
a(100) = 7 because 100^9 + 7^2 = 1000000000000000049 = 157 * 6369426751592357 and for no smaller k>0 is 100^9 + k^2 a semiprime.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A001358, A108714, A109197, A109198, A109199, A109200, A109201, A109202, A109203.

Programs

Mathematica

a[n_] := (For[k = 1, PrimeOmega[n^9 + k^2] != 2, k++]; k); a /@ Range[0, 88] (* Giovanni Resta, Jun 17 2016 *)

PARI

a(n) = my(k=1); while(bigomega(n^9+k^2)!=2, k++); k \\ Felix Fröhlich, Jun 17 2016

Extensions

a(15) corrected by Giovanni Resta, Jun 17 2016